Question

If in a circular coil $A$ of radius $R,$ current $i$ is flowing and in another coil $B$ of radius $2 R$ a current $2 i$ is flowing, then the ratio of the magnetic fields, $B_{A}$ and $B_{B}$ produced by them will be :

• A. 1
• B. 2
• C. $1 / 2$
• D. 4

Answer 1

Answer: (A)

1

Answer 2

Magnetic field in circular coil $A$ is $B_{A}=\frac{\mu_{0} N i}{2 R}$ where $R$ is radius and $i$ is current flowing in coil. Similarly $B_{B}=\frac{\mu_{0} N(2 i)}{2 \cdot(2 R)}$ $=\frac{\mu_{0} N i}{2 R}$ $\therefore \frac{B_{A}}{B_{B}}=\frac{1}{1}=1$